Intrinsic line density
The intrinsic density (also intrinsic carrier density ) is the characterizing material property of a semiconductor, in view of its electrical conductivity . It describes the charge carrier density of an ideal semiconductor that is undisturbed in its crystal lattice . The associated management mechanism is called intrinsic management .
The intrinsic conduction density determines the minimum value of the electrical conductivity. The actual conductivity of the semiconductor can be higher due to contamination or set to a higher value by doping . The conduction of impurities caused by this generally exceeds the conduction by several orders of magnitude at room temperature ; it thus covers the property of the base material.
In semiconductors, all electrons are bound to the crystal atoms at absolute zero . Only when the temperature rises is sufficient thermal energy available to raise individual electrons to the energy level of the conduction band . The released electrons and the remaining defect electrons ( holes ) are available for charge transport (generation of electron-hole pairs ); This effect is countered by the recombination of electron-hole pairs with the release of energy .
In thermodynamic equilibrium , there is an equilibrium between generation and recombination: the number density of freely moving charge carriers is constant over time. The intrinsic conduction density is thus composed of the average number density of free electrons and holes at the respective temperature:
|semiconductor||in cm −3|
|Gallium arsenide (GaAs)||
- (Law of mass action )
- : Electron density
- : Hole density
- , : effective density of states in conduction and valence bands
- : Energy of the lower edge of the conduction band
- : Energy of the upper edge of the valence band
- : Band gap
- : chemical potential
- : Boltzmann constant
- : absolute temperature
This gives the intrinsic conduction density:
This result is significantly dependent on the temperature . The corresponding diagram does not take into account that , and also depend on the temperature, but not as pronounced. In the area of room temperature, it roughly doubles when the temperature increases by 10 K.
State in real crystals
It should be noted that there is no such thing as a perfect crystal ( entropy argument of thermodynamics ). At an atomic density of about 5e22 cm −3 (guide value for silicon and germanium) would result in an impurity density of 5e13 cm −3 means that there is a single disturbance in the crystal lattice for every billion atoms of the semiconductor. But even a crystal that is so poor in defects is not yet poor enough for the state of intrinsic conduction. Conversely,the charge carrier density and thus the conductivitycan be increased by extrinsic impurities (doping). The typical density of the introduced foreign atoms is 10 14 −10 18 cm −3 .
Since the degree of ionization of the impurities increases with the temperature, the charge carrier density initially increases with the temperature ( impurity reserve ). At room temperature (in the case of silicon) all impurities are normally ionized ( impurity depletion ), and the charge carrier density no longer depends on the temperature, but on the doping concentration; this case is called extrinsic conductivity .
If the temperature is increased further, the semiconductor loses its character as n-doped or p-doped, since more and more charge carriers are generated by the intrinsic charge carrier generation. The semiconductor material becomes intrinsically conductive because the thermal energy is now sufficient to excite electrons from the valence band to the conduction band to a greater extent. The practical use of doped semiconductor components is therefore only sufficient for germanium up to 70 ° C and for silicon up to about 170 ° C or in a temperature range typically −40 ° C <<160 ° C. A calculation for the intrinsic conduction density of silicon at 700 K comes to 6.3e15 cm−3.
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